Call an attorney before you do anything. In some states, like mine, if there isn’t a written lease, the law regarding tenants applies. When the rented place is the person’s home, you have to give notice not less than the frequency of the rental payment or 30days, whichever is longer. In addition, the notice must be given before the next payment date, with the termination being the one after that. If the tenant doesn’t leave, you can then file what here is called an ejectment action, and get a judgment, and the sheriff will throw him and the girlfriend out and put their stuff on the street.
I have had a lot of experience, professionally, with people like your tenant, and you can’t fix them. You aren’t likely to outwit them because people like that usually know better than you do what you can and can’t do. They’ve been around. You just have to get rid of them. Call a lawyer and get your notice running.
The good thing is that a lot of those kind will get out right before the court date, or even after the deputy serves a summons on them. If they’re doing anything illegal, and they likely are, they don’t want the attention of the law focused on them.